The B-Adic Diaphony of Digital (T, S)-Sequences

The b-adic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this article we give an upper bound on the b-adic diaphony of digital (T, s)-sequences over Z b. And we derive a condition on the quality function T such that the b-adic diaphony of the digital (T, s)-sequence over Z b is of order O((log N)s/2N−1). We also give a metrical result; for µs-almost all generators of a digital (T, s)-sequence over Z b the b-adic diaphony of the sequence is of order O((log log N)2(log N)3s/2N−1).